Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Lee J.M. — Introduction to Topological Manifolds
Lee J.M. — Introduction to Topological Manifolds



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Introduction to Topological Manifolds

Автор: Lee J.M.

Аннотация:

This book is an introduction to manifolds at the beginning graduate level. It contains the essential topological ideas that are needed for the further study of manifolds, particularly in the context of differential geometry, algebraic topology, and related fields. Its guiding philosophy is to develop these ideas rigorously but economically, with minimal prerequisites and plenty of geometric intuition. A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. Unlike algebra and analysis, which all math majors see as undergraduates, manifolds enter the curriculum much later. It is even possible to get through an entire undergraduate mathematics education without ever hearing the word "manifold." Yet manifolds are part of the basic vocabulary of modern mathematics, and students need to know them as intimately as they know the integers, the real numbers, Euclidean spaces, groups, rings, and fields. In his beautifully conceived introduction, the author motivates the technical developments to follow by explaining some of the roles manifolds play in diverse branches of mathematics and physics. Then he goes on to introduce the basics of general topology and continues with the fundamental group, covering spaces, and elementary homology theory. Manifolds are introduced early and used as the main examples throughout. John M. Lee is currently Professor of Mathematics at the University of Washington.


Язык: en

Рубрика: Математика/Геометрия и топология/Общая топология/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 385

Добавлена в каталог: 19.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
Solid geometry      7
South pole      45
Space      18
Space, curve      2
Space, discrete      19
Space, Euclidean      347
Space, Hausdorff      31
Space, identification      52
Space, metric      348
Space, product      48
Space, quotient      52
Space, topological      18
Space, variable      152
Space-filling curve      188
Spacetime      14
Spacetime, homogeneous and isotropic      14
Special linear group      11
Special loop      190
Special orthogonal group      11
Special unitary group      11
Specification axiom      338
Sphere      3 44
Sphere is simply connected      217
Sphere with n handles      129
Sphere, Euler characteristic      143
Sphere, fundamental group      188
Sphere, not a retract of the ball      334
Sphere, presentation      133
Sphere, quotient of disk      120
Sphere, quotient of square      120
Sphere, singular homology      309
Sphere, turning inside out      5
Sphere, unit      23 44
Sphere, unit in $\mathbb{R}^3$      3
Square root, complex      8
Stable trajectory      14
Stack of pancakes      234
Standard basis for $\mathbb{Z}^n$      204
Standard presentation      133 137
Standard simplex      292
Star, open      114
Star-shaped      162
Steinitz, Ernst      112
Stereographic projection      45 62 187
Stereographic projection and one-point compactification      89
Straight-line homotopy      150
Strictly increasing      345
String      15
String, theory      14
Strong deformation retract      161
Strong deformation retraction      161
Structure theorem, covering group      250
SU(n) (special unitary group)      11
Subbasis      36
Subcategory      171
Subcategory, full      171
Subcomplex of a Euclidean simplicial complex      95
Subcomplex of an abstract simplicial complex      96
Subcover      32 73 350
Subcover, countable      32
Subdividing      133
Subdivision      109
Subdivision, barycentric      110 315
Subdivision, elementary      112
Subdivision, operator, singular      316
Subgraph      101
Subgroup      353
Subgroup of a cyclic group      357
Subgroup of a free abelian group      205
Subgroup of a topological group      59 61 63
Subgroup, normal      354
Subsequence      345
Subset      338
Subset of a countable set      344
Subset, proper      338
subspace      39 40
Subspace of a metric space      40
Subspace of a subspace      41
Subspace, affine      92
Subspace, closed sets      41
Subspace, Hausdorff      42
Subspace, second countable      42
Subspace, topology      40
Subspace, topology, basis for      42
Subspace, topology, characteristic property      41
Subspace, topology, uniqueness      47
Sum in a category      175
Sum in a category, uniqueness      175
Sum in the category of groups      199
Sum in the topological category      177
Sum, connected      126
Sum, connectedis a manifold      126
Sum, connectedwith sphere      129
Sum, direct      177
Supremum      343
surface      3 117 119
Surface of genus n      144
Surface of revolution      45
Surface, classification      6
Surface, fundamental group of      220
Surface, fundamental group of, abelianized      228
Surface, nonorientable      144
Surface, orientable      144
Surface, presentation      132
Surface, presentation and fundamental group      217
Surface, presentation, classification      137
Surface, Riemann      9
Surface, universal covering of      282
Surjective      342
symmetric      340
Symmetric group      353
Symmetry of a metric      348
Terminal point of a path      150
Terminal vertex      131
tetrahedron      92
Theta space      162
Thurston geometrization conjecture      7
Thurston, William      7
Tietze, Heinrich      112 203
time variable      152
Tofu sandwich theorem      254
TOP (topological category)      171
Topological boundary      35
Topological category      171
Topological category, pointed      171
Topological embedding      40
Topological group      58
Topological group, discrete      58
Topological group, discrete subgroup of      270
Topological group, fundamental group of      191
Topological group, product of      59
Topological group, quotient of      63
Topological group, subgroup of      59 63
Topological group, universal covering space of      290
Topological invariance of Euler characteristic      327
Topological invariance of homology groups      296
Topological invariance of the fundamental group      159
Topological invariant      6
Topological manifold      33
Topological property      4 22
Topological space      18
Topologically equivalent      4 22
Topologically equivalent, presentations      133
Topologist’s sine curve      69 72 88
topology      4 18
Topology, algebraic      6
Topology, discrete      19
Topology, disjoint union      37
Topology, euclidean      19
Topology, generated by a basis      27
Topology, generated by a subbasis      36
Topology, metric      19
Topology, product      48
Topology, quotient      52
Topology, relative      40
Topology, subspace      40
Topology, trivial      19
Torsion, element      205
Torsion, free      205
Torsion, subgroup      205
Torus      3 51
Torus as a quotient of the square      55 79
Torus, coverings of      270 286
Torus, Euler characteristic      143
Torus, fundamental group      189 220
Torus, homeomorphic to doughnut surface      51 80
Torus, n-dimensional      51
Torus, n-dimensional, coset space of $\mathbb{R}^n$      61
Torus, n-holed      129
Torus, presentation      133
Total ordering      341
Totally ordered set      37 341
Trajectory, periodic      14
Trajectory, stable      14
Transformation, elementary      133
Transformation, linear      20
Transitive      340
Transitive, group action      60
Transitivity of covering group      249
Translation, left      59 63
Translation, right      59
Transpose of linear map      173
Transposition      353
TREE      163
Tree, contractible      163
Tree, maximal      214
Triangle inequality      89 348
Triangle inequality for hyperbolic metric      289
Triangle, Euclidean      7
Triangulable      100
Triangulation      100
Triangulation of 1-manifolds      102
Triangulation of 2-manifolds      104
Triangulation of 3-manifolds      105
Trigonometric function      20
Trivial group      353
Trivial topology      19
Turning the sphere inside out      5
Twisted edge pair      139
Two origins, line with      62
Tychonoff’s theorem      75
Type, homotopy      161
U(n) (unitary group)      11
Uncountable set      344
Unfolding      135
Union of an indexed collection      345
Union of closed sets in a metric space      349
Union of closed sets in a topological space      24
Union of open sets in a metric space      349
Union of open sets in a topological space      18
Union of sets      339
Union, axiom      339
Union, connectedness of      67
Union, countable      344
Union, disjoint      340 345
Union, disjoint, topology      37
Unique lifting property      237
Unique lifting property of the circle      181
Uniqueness of abelianization      231
Uniqueness of covering spaces      260
Uniqueness of free abelian group      208
Uniqueness of free group      201
Uniqueness of free product      199
Uniqueness of product topology      49
Uniqueness of quotient spaces      57
Uniqueness of subspace topology      47
Unit ball in $\mathbb{R}^n$      22
Unit circle      45
Unit interval      54
Unit sphere      23 44
Unitary group      11
Unitary group, special      11
Universal coefficient theorem      330
Universal covering      261
Universal covering of a topological group      290
Universal covering of compact surfaces      282
Universal covering of n-holed torus      275
Universal covering, space      261
Universal covering, space, existence      262
Universal mapping properties      174
Upper bound      341
Upper half space      34
Variety, algebraic      12
VECTc (category of complex vector spaces)      171
Vector field      192 322
Vector field, index      192
Vector space      347
Vector space, free      97
Vector spaces, complex, category of      171
Vector spaces, real, category of      171
VECTr (category of real vector spaces)      171
Vertex of a presentation      131
Vertex of a simplex      92
Vertex of an abstract simplicial complex      96
Vertex, initial      131
Vertex, map      95 96
Vertex, point      124
Vertex, scheme      96
Vertex, terminal      131
Vertices      see “Vertex”
Volume      7 254
Wedge of spaces      55
Wedge of spaces, fundamental group, singular homology      334
Well-ordered      88 341
Well-ordering theorem      88 346
Winding number      179 182
Word      130 194
Word, empty      194
Word, problem      203
Word, reduced      195
World sheet      15
Zero-dimensional, Euclidean space      31 347
Zero-dimensional, homology      298
Zero-dimensional, manifold      37
Zigzag lemma      310
Zorn’s Lemma      347
1 2 3 4 5 6
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте